{"id":2342,"date":"2019-11-01T14:51:08","date_gmt":"2019-11-01T14:51:08","guid":{"rendered":"http:\/\/mentalblocks.co.uk\/blog\/?p=2342"},"modified":"2019-11-01T15:11:15","modified_gmt":"2019-11-01T15:11:15","slug":"carnival-of-mathematics-175-sum-square-over-the-rainbow","status":"publish","type":"post","link":"http:\/\/mentalblocks.co.uk\/blog\/carnival-of-mathematics-175-sum-square-over-the-rainbow\/","title":{"rendered":"Carnival of Mathematics 175 – Sum Square Over The Rainbow"},"content":{"rendered":"\n

You might be wondering what a couple of knitters are doing hosting the Carnival of Mathematics. If you are not familiar with the methods we use to teach maths you might want to check out our main Woolly Thoughts<\/a> site. It has got rather rambling over the last 20+ years. The Afghans page<\/a> is a good place to start.<\/p>\n\n\n\n

First things first – the number 175.<\/strong><\/p>\n\n\n\n

Steve and I often talk about ‘nice numbers’. That usually means numbers that can be split up nicely when designing things – numbers with lots of factors (or divisors or whatever else you want to call them) or other interesting properties. <\/p>\n\n\n\n

At first glance 175 looks like a nice number. It’s a number you come across quite often. It’s a multiple of 25. That has to make it a nice useful number.<\/p>\n\n\n\n

Look at it more closely. Is it really much use? I don’t think so. It’s 5 x 5 x 7. Fives are OK but I don’t like Sevens. The only time we have used seven in designs is for rainbows. <\/p>\n\n\n\n

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I do quite like that 11<\/sup> + 72<\/sup> + 53<\/sup> = 175. Wikipedia<\/em> tells me that 135, 518, 598, and 1306 also have this property where raising the digits to powers of successive integers, and adding, equals itself. <\/p>\n\n\n\n

Fives makes me think of pentominoes. I wondered whether there was some connection between the number 175 and the five squares that make up a pentomino. There isn’t but 5 x (5 + 7) does give me the total number of squares in a set of pentominoes. <\/p>\n\n\n\n

Wikipedia<\/em> also tells me
175 is an odd number<\/a>, a composite number<\/a>, and a deficient number<\/a>. It is a decagonal number<\/a>, a 19-gonal number<\/a>, and a centered 29-gonal number<\/a>.<\/p>\n\n\n\n

175 is an Ulam number<\/a>, and a Zuckerman number<\/a>. It is the magic constant<\/a> of the n<\/em>\u00d7n<\/em> normal magic square<\/a> and n-Queens Problem<\/a> for n = 7.<\/p>\n\n\n\n

… and now for the Carnival<\/strong><\/p>\n\n\n\n